The triangle has a base along the y axis of length 8 and a height along the x axis of length 5, so the area is (1/2)8*5=20.
The reasoning is:
To find out where the lines intersect, multiply the second equation by 5 and add to the first: 8x=40, so x=5 and therefore y=0. The intersection is (5,0) on the x axis. The first line intersects the y axis when x=0 at y=3. So (0,3) is a vertex of the triangle. It intersects the x axis when y=0 at x=5, which is also the point where the lines intersect. So (5,0) is another vertex. The second line has a y intercept of -5, so (0,-5) is the third vertex. Part of the base of the triangle is part of the y axis from 0 to 5 and the other part of the base extends from the origin (0,0) to (0,-5). The difference between (0,3) and (0,-5) is 8, the length of the base. The line from (0,0) to (5,0) is the height of length 5. We therefore have the base and height so we get from these the area of the triangle as above: 20.